Even with contacts this is still a problem for me in the strong Australian sun.
Using one hand to cover the eyepiece is a technique I sometimes use (this is not ideal). The towel over the head would be a good idea, although you may find yourself in the local lockup
The other method is to get a "rough" reading using the top LED and then use preview to check the histogram.
I have noticed that the contents of the viewfinder become brighter / darker depending on the strength of the light. Unfortunately though, not bright enough.
I have seen a couple of posts showing an attachment to put on the eyepiece and was wondering if that would help.
Regards
Bob